Stability of symmetric vortices for two-component Ginzburg–Landau systems

We study Ginzburg–Landau equations for a complex vector order parameter Ψ=(ψ+,ψ−)∈C2Ψ=(ψ+,ψ−)∈C2. We consider the Dirichlet problem in the disk in R2R2 with a symmetric, degree-one boundary condition, and study its stability, in the sense of the spectrum of the second variation of the energy. We find that the stability of the degree-one equivariant solution depends on the Ginzburg–Landau parameter as well as the sign of the interaction term in the energy.